- which image do you use?
- which Arduino IDE version do you use?
- which Galileo board do you have - did you select the right board?
you might try a simple sketch which e.g. outputs something to Arduino IDE serial (e.g. system("echo 'Hello World' > /dev/ttyGS0");) just to check whether sketches are started in general [maybe put a delay(5000); before to give you some time to open the serial within the IDE]
if you do have access to the board (serial or ssh):
- has the /sketch/sketch.elf file been put in place?
- can you execute /sketch/sketch.elf from within console?